A hydraulics problem uses Rectangular weir discharge. Given weir coefficient (C) = 3.2500; weir length (L) = 9.0000 ft; head over weir (H) = 0.9500 ft, determine the discharge (Q) in cfs.

Start with the thinking

• The governing relation printed in this handbook section is Rectangular weir discharge.
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C L H^{3/2}$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3 — List the givens: weir coefficient (C) = 3.2500, weir length (L) = 9.0000 ft, head over weir (H) = 0.9500 ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Q = 27.0839\ \text{cfs}$$

6. Step 6 — Check: returning Q = 27.0839 cfs to

   $$Q = C L H^{3/2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 54.1678 — kept a factor of two that cancels in the correct rearrangement.
• 13.5420 — dropped that same factor in the other direction.
• 29.7923 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → V-Notch

A hydraulics problem uses Rectangular weir discharge. Given weir length (L) = 18.0000 ft; head over weir (H) = 1.4500 ft; discharge (Q) = 197.6 cfs, determine the weir coefficient (C).

Start with the thinking

• The governing relation printed in this handbook section is Rectangular weir discharge.
• Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C L H^{3/2}$$

2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

3. Step 3 — List the givens: weir length (L) = 18.0000 ft, head over weir (H) = 1.4500 ft, discharge (Q) = 197.6 cfs.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C = 6.2873$$

6. Step 6 — Check: returning C = 6.2873 to

   $$Q = C L H^{3/2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 12.5745 — kept a factor of two that cancels in the correct rearrangement.
• 3.1436 — dropped that same factor in the other direction.
• 6.9160 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → V-Notch

A hydraulics problem uses Rectangular weir discharge. Given weir coefficient (C) = 3.0000; head over weir (H) = 1.9500 ft; discharge (Q) = 418.5 cfs, determine the weir length (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Rectangular weir discharge.
• Everything except L is given, so isolate L symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C L H^{3/2}$$

2. Step 2 — Rearrange the relation so that L stands alone on the left-hand side.

3. Step 3 — List the givens: weir coefficient (C) = 3.0000, head over weir (H) = 1.9500 ft, discharge (Q) = 418.5 cfs.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$L = 51.2298\ \text{ft}$$

6. Step 6 — Check: returning L = 51.2298 ft to

   $$Q = C L H^{3/2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 102.5 — kept a factor of two that cancels in the correct rearrangement.
• 25.6149 — dropped that same factor in the other direction.
• 56.3527 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → V-Notch

A hydraulics problem uses Rectangular weir discharge. Given weir coefficient (C) = 3.4500; weir length (L) = 9.0000 ft; head over weir (H) = 0.8000 ft, determine the discharge (Q) in cfs.

Start with the thinking

• The governing relation printed in this handbook section is Rectangular weir discharge.
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C L H^{3/2}$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3 — List the givens: weir coefficient (C) = 3.4500, weir length (L) = 9.0000 ft, head over weir (H) = 0.8000 ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Q = 22.2176\ \text{cfs}$$

6. Step 6 — Check: returning Q = 22.2176 cfs to

   $$Q = C L H^{3/2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 44.4351 — kept a factor of two that cancels in the correct rearrangement.
• 11.1088 — dropped that same factor in the other direction.
• 24.4393 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → V-Notch

A hydraulics problem uses Rectangular weir discharge. Given weir length (L) = 10.0000 ft; head over weir (H) = 2.0000 ft; discharge (Q) = 391.4 cfs, determine the weir coefficient (C).

Start with the thinking

• The governing relation printed in this handbook section is Rectangular weir discharge.
• Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C L H^{3/2}$$

2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

3. Step 3 — List the givens: weir length (L) = 10.0000 ft, head over weir (H) = 2.0000 ft, discharge (Q) = 391.4 cfs.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C = 13.8381$$

6. Step 6 — Check: returning C = 13.8381 to

   $$Q = C L H^{3/2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 27.6762 — kept a factor of two that cancels in the correct rearrangement.
• 6.9190 — dropped that same factor in the other direction.
• 15.2219 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → V-Notch

A hydraulics problem uses Rectangular weir discharge. Given weir coefficient (C) = 3.1000; head over weir (H) = 2.6000 ft; discharge (Q) = 144.2 cfs, determine the weir length (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Rectangular weir discharge.
• Everything except L is given, so isolate L symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C L H^{3/2}$$

2. Step 2 — Rearrange the relation so that L stands alone on the left-hand side.

3. Step 3 — List the givens: weir coefficient (C) = 3.1000, head over weir (H) = 2.6000 ft, discharge (Q) = 144.2 cfs.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$L = 11.0954\ \text{ft}$$

6. Step 6 — Check: returning L = 11.0954 ft to

   $$Q = C L H^{3/2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 22.1908 — kept a factor of two that cancels in the correct rearrangement.
• 5.5477 — dropped that same factor in the other direction.
• 12.2050 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → V-Notch

A hydraulics problem uses Rectangular weir discharge. Given weir coefficient (C) = 3.2500; weir length (L) = 9.5000 ft; head over weir (H) = 0.8000 ft, determine the discharge (Q) in cfs.

Start with the thinking

• The governing relation printed in this handbook section is Rectangular weir discharge.
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C L H^{3/2}$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3 — List the givens: weir coefficient (C) = 3.2500, weir length (L) = 9.5000 ft, head over weir (H) = 0.8000 ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Q = 22.0924\ \text{cfs}$$

6. Step 6 — Check: returning Q = 22.0924 cfs to

   $$Q = C L H^{3/2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 44.1847 — kept a factor of two that cancels in the correct rearrangement.
• 11.0462 — dropped that same factor in the other direction.
• 24.3016 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → V-Notch

A hydraulics problem uses Rectangular weir discharge. Given weir length (L) = 12.5000 ft; head over weir (H) = 2.4000 ft; discharge (Q) = 319.5 cfs, determine the weir coefficient (C).

Start with the thinking

• The governing relation printed in this handbook section is Rectangular weir discharge.
• Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C L H^{3/2}$$

2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

3. Step 3 — List the givens: weir length (L) = 12.5000 ft, head over weir (H) = 2.4000 ft, discharge (Q) = 319.5 cfs.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C = 6.8745$$

6. Step 6 — Check: returning C = 6.8745 to

   $$Q = C L H^{3/2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 13.7491 — kept a factor of two that cancels in the correct rearrangement.
• 3.4373 — dropped that same factor in the other direction.
• 7.5620 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → V-Notch

A hydraulics problem uses Rectangular weir discharge. Given weir coefficient (C) = 3.0000; head over weir (H) = 0.5000 ft; discharge (Q) = 142.0 cfs, determine the weir length (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Rectangular weir discharge.
• Everything except L is given, so isolate L symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C L H^{3/2}$$

2. Step 2 — Rearrange the relation so that L stands alone on the left-hand side.

3. Step 3 — List the givens: weir coefficient (C) = 3.0000, head over weir (H) = 0.5000 ft, discharge (Q) = 142.0 cfs.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$L = 133.9\ \text{ft}$$

6. Step 6 — Check: returning L = 133.9 ft to

   $$Q = C L H^{3/2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 267.8 — kept a factor of two that cancels in the correct rearrangement.
• 66.9394 — dropped that same factor in the other direction.
• 147.3 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → V-Notch

A hydraulics problem uses Rectangular weir discharge. Given weir coefficient (C) = 3.2000; weir length (L) = 4.0000 ft; head over weir (H) = 0.8500 ft, determine the discharge (Q) in cfs.

Start with the thinking

• The governing relation printed in this handbook section is Rectangular weir discharge.
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = C L H^{3/2}$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3 — List the givens: weir coefficient (C) = 3.2000, weir length (L) = 4.0000 ft, head over weir (H) = 0.8500 ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Q = 10.0309\ \text{cfs}$$

6. Step 6 — Check: returning Q = 10.0309 cfs to

   $$Q = C L H^{3/2}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 20.0617 — kept a factor of two that cancels in the correct rearrangement.
• 5.0154 — dropped that same factor in the other direction.
• 11.0340 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → V-Notch